In conventional blood gas analysis machines, a sample of blood withdrawn from a patient is heated to a reference temperature of 37.degree. C. before the partial pressure of oxygen (pO.sub.2) is determined. Over time, the medical community has thus developed a preference for reporting all pO.sub.2 measurements referenced to 37.degree. C. However, when pO.sub.2 is measured in vivo instead of in a blood gas analyzer, the measurement is often made at a substantially different temperature even though 37.degree. C. is normal body temperature. For example, during certain surgical procedures, it is necessary to lower the patient's body temperature by as much as 20.degree. C., thereby depressing metabolic activity. If the pO.sub.2 measurement is made while the patient's body is chilled, the result is very different than a corresponding measurement made at 37.degree. C. An anesthesiologist controlling the administration of oxygen and other gases to the patient typically prefers to record the pO.sub.2 at the accepted reference temperature of 37.degree. C. rather than the lower measurement. Moreover, the anesthesiologist may prefer to base decisions concerning the patient's condition on pO.sub.2 data referenced to 37.degree. C. When making such decisions during a critical operation, the anesthesiologist may not have time to draw a sample of blood for analysis in a blood gas analyzer at the reference temperature. An in vivo, real time determination of pO.sub.2 is sometimes essential, even if carried out at a different measurement temperature than the desired 37.degree. C. reference.
Conversion between a pO.sub.2 measurement at one temperature to that at another temperature is not a trivial task. The solubility of oxygen in blood as a function of temperature is determined by a non-algebraic combination of transcendental functions. As a result, it is not possible to analytically solve a simple equation to convert a pO.sub.2 measurement at a substantially different temperature to a corresponding value at the desired reference temperature of 37.degree. C. In the past, medical personnel have been forced to manually convert a measured value for pO.sub.2 to the 37.degree. C. reference temperature using a nomogram or by interpolating values from a look-up table. Neither of these techniques are particularly desirable when speed in determining the data is essential; furthermore, any human errors in the conversion process can have potentially life-threatening consequences.
The complex relationship between temperature and pO.sub.2 is evident from the equation that has been developed in the prior art to convert from a pO.sub.2 measurement made at 37.degree. C. to a different temperature. This equation is reported by R. A. Ashwood, G. Kost, and M. Kenny in "Temperature Correction of Blood-Gas and pH Measurements," Clinical Chemistry, Vol. 29, 11:1877-1885, 1983 and by J. W. Severinghaus in "Simple, Accurate Equations for Human Blood O.sub.2 Dissociation Computations," American Journal of Physiology, Vol. 46, 3:599-602. The equation in both of these references is as follows: ##EQU1## where pO.sub.2PT is the predicted partial pressure of oxygen at a temperature T that is different than the reference temperature, and pO.sub.2REF is the measured partial pressure of oxygen at the reference temperature (37.degree. C.). One might assume that equation 1 could simply be rearranged to determine pO.sub.2 at the reference temperature from the pO.sub.2 measured at a temperature different than the reference temperature, i.e., as follows: ##EQU2## where pO.sub.2M is the partial pressure of oxygen measured at the temperature T. However, Equation 2 produces erroneous results due to the nature of the mathematical relationship between measurement temperature and pO.sub.2. In the above-noted paper, Severinghaus recognized the difficulty of calculating pO.sub.2 at 37.degree. C. based on measurements made at other temperatures. On page 600 of the Journal, he suggests that, "[t]o begin with some other temperature, one may estimate a trial 37.degree. C. pO.sub.2 using the factors 6%/.degree.C. if pO.sub.2 &lt;100, and 6 Torr/.degree.C. above 100 Torr, and proceed iteratively in Eq. (3)." (Equation 3 in the reference is equivalent to Equation 1, above.) What Severinghaus intended by this statement is not entirely clear, because he did not present any example of how the iterative process is carried out nor any support for its efficacy in producing an accurate result.
Accordingly, a method is required for quickly determining the pO.sub.2 of a patient's blood at the reference temperature, based on a measurement made at another temperature. The method should be automatically carried out to avoid human error and must be implemented quickly (in real time) to make the results of an in vivo measurement of pO.sub.2 at the patient's temperature immediately available as a corresponding value at the reference temperature during critical medical procedures.